Mathmatical Thinking

These were the four words written on a course evaluation at the end of Dana’s introduction to proof course from the spring 2013 semester. We believe that this perfectly captures the essence of an effective inquiry-based learning (IBL) experience for a student. Dana couldn’t ask for a better student comment. He should retire now; it’s all downhill from here. The “big” IBL conference is the annual Legacy of R. As we reflect on this year’s conference, “try, fail, understand, win” provides a good outline of the lessons learned.

Try: We try something new in our classrooms.We try to engage our students in mathematics and inspire them to crave more.We try to provide our students with a safe environment where they are willing to take risks.We try to relinquish control, sit back, and see what our students can do.Fail:
Telling You the Answer Isn't the Answer. This is a story from my class.

The course is a physics course designed for elementary education majors. Really, it’s a great course using a great curriculum – Physics and Everyday Thinking. The basic idea is that students work in groups to collect evidence from different experiments. They use this evidence to build models about force, motion, energy, circuits and stuff like that. One of the important parts of the course is that students have a chance to build ideas and struggle with the model-building process. Here is how a typical discussion might go. The discussion then goes something like this: Student 1: I think that if the ball is slowing down, it has to have unbalanced forces. Student 2: I’m not so sure. Student 3: Both of these ideas seem reasonable. It happens every semester.

(“I want to be a princess! No, I’m gonna be Cinderella? I changed my mind, I want to be a fairy! Elsa! Alice in Wonderland!”) Cue the collective groans of parents across the land—especially feminist ones. A Google search for “boy Halloween costume ideas” reveals a wide range of options—dinosaurs, vampires, ninjas. Simply put, the popular costume options for young girls are unoriginal and highly sexualized—and just steps away from the overtly sexy costumes ideas for teen and adult women. Expanding the list of “what girls can be for Halloween” is one small step toward expanding the list of “what girls can be”—period.

Look: I’m not saying that girls shouldn’t dress as magical pink tutu-clad fairy princesses. Why not do the same on Halloween—for your kid or for yourself? Dressing up as an unsung woman from history is a great opportunity to have fun and educate others at the same time. Angela Davis Dolores Huerta. Part 1. In Part 1 of a series, I focus on the distinction between high school math and university-level mathematics, suggesting they are effectively different subjects that are best learned in different ways.

One of the biggest obstacles in giving an online course on mathematical thinking, which my MOOC is, is coping with the expectations students bring to the course – expectations based in large part on their previous experience of mathematics classes. To be sure, prior expectations are often an issue for regular, physical classes. But there the students have an opportunity to interact directly with the instructor on a regular basis. They also have the benefit of a co-present support group of others taking the same class. But in a massive open online class, apart from locally configured support groups and text-based discussions on the MOOC platform discussion forum, each student is pretty much on her or his own. Not only is the subject matter different, so too is the pedagogy.
Let's teach the world.